Exploration: Exponential Functions and Derivatives - How NOT to Compute the Derivative

One very common mistake in computing the derivative of the exponential f(x)=ex is to use the Power Rule for derivatives, rather than the formula f '(x)=ex. To see why the Power Rule does not work, consider what the resulting derivative would be, using the Power Rule: f '(x)=x ex-1 (please keep in mind that this is incorrect). Using the functions f(x)=ex and f '(x)=x ex-1 in the same applet as on the previous page, it is easy to see that the values of this "derivative" do not give slopes of tangent lines to the graph of f '(x):